Precalculus: Mathematics for Calculus - 6th Edition
Precalculus: Mathematics for Calculus - 6th Edition
6th Edition
ISBN: 9780840068071
Author: Stewart, James, Redlin, Lothar, Watson, Saleem
Publisher: Cengage Learning
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Textbook Question
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Chapter 5.6, Problem 43E

Electric Generator The graph shows an oscilloscope reading of the variation in voltage of an AC current produced by a simple generator.

  1. (a) Find the maximum voltage produced.
  2. (b) Find the frequency (cycles per second) of the generator.
  3. (c) How many revolutions per second does the armature in the generator make?
  4. (d) Find a formula that describes the variation in voltage as a function of time.

Chapter 5.6, Problem 43E, Electric Generator The graph shows an oscilloscope reading of the variation in voltage of an AC

(a)

Expert Solution
Check Mark
To determine

The value of maximum voltage produced by the generator.

Explanation of Solution

The graph which shows the variation of voltage of an AC current produced by a simple generator is given below.

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 5.6, Problem 43E , additional homework tip 1

Figure (1)

From the Figure (1), it is noticed that the maximum voltage of the curve lies on the y-axis at 45.

Thus, the value of maximum voltage is 45V .

(b)

Expert Solution
Check Mark
To determine

The frequency of the generator.

Explanation of Solution

The graph for the voltage is variation is given below.

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 5.6, Problem 43E , additional homework tip 2

Figure (1)

From the Figure (1) it is noticed that the period of the sine curve is 0.1 . In period of 0.1 there are 4 cycles.

Thus, the frequency of the sine curve is defined as, 4 cycles/0.1s or 40cycles/s which is the frequency of the generator.

(c)

Expert Solution
Check Mark
To determine

The number of revolution per second the armature takes in the generator.

Explanation of Solution

The one revolution of the armature generates one cycle of voltage.

The frequency of the voltage is 40cycles/s .

one revolution of armature= one cycle of voltage

So, the value of one revolution of armature is 40 revolutions/s .

(d)

Expert Solution
Check Mark
To determine

The formula that describes the variation in voltage as a time function.

Explanation of Solution

The graph for the voltage is variation is given below,

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 5.6, Problem 43E , additional homework tip 3

Figure (1)

From the Figure (1) it is noticed that the period of the sine curve is 0.1 . In period of 0.1 there are 4 cycles and the amplitude and frequency of the function is 45 V, 40 cycles/s .

Since the waves starts from positive 45 then, the formula of frequency,

f=ω2π

Substitute 40 for f in the above formula,

40=ω2π40⋅2π=ω80π=ω

The general equation for simple harmonic motion is,

f(x)=acosωt (1)

Substitute 80π for ω , 45 for a in equation (1),

V(t)=45cos80πt

Thus the general formula of voltage variation is V(t)=45cos80πt .

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Chapter 5.6, Problem 42E
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Chapter 5.6, Problem 44E

Chapter 5 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

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